SplittingTemplates

The splitting templates parameterize the sub-jet kinematics subject to the constraint that the combined jet mass and energy are conserved. This is done in the frame of \(p_\mu = (E, p_T, 0, 0)\)

The subjets can then be described by 4 degrees-of-freedom: (\(\theta_A\). zA, mA, mB). Where subjet A is the subjet with higher \(z = p \cdot \hat{p}_{combined}\). Theta_A is the angle between this jets direction and the direction of the combined jet. The plane of the decay is a 5th DoF. Apart from \(\theta_A\) and zA, the 5 variable are not very correlated. So we can sample this same as a product of 2D x 1D x 1D x 1D randomly sampled variables.

Note that randomly sampling from the splitting templates will change the combined jets mass (which is of course a function of its substructure.)